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NCERT Solutions for Class 7th Maths Chapter 6 In-text Questions — Tiling

Book page 157 Updated on2026-09-19

Q1.
Can a 4 × 6 grid be tiled using multiple copies of 2 × 1 tiles? We are allowed to rotate a 2 × 1 tile and use it.
Answer

Yes. It takes 12 tiles, and there are many ways to do it.

Number of unit squares = 4 × 6 = 24
Each 2 × 1 tile covers 2 squares
Number of tiles needed = 24 ÷ 2 = 12

An easy tiling. The grid has 4 rows, an even number. So fill every column from top to bottom with 2 vertical tiles: 2 tiles per column × 6 columns = 12 tiles. No gaps, no overlaps.

Why it happens: a vertical tile is exactly 2 rows tall. If the number of rows is even, a column of that height is a whole number of tiles. Here 4 ÷ 2 = 2 tiles per column, and the same trick works for every column.
Tip: the book's picture uses a mixture of horizontal and vertical tiles. That is fine — an even count of squares plus a workable arrangement is all a tiling needs, and there is no single "right" answer.
Q2.
Can a 4 × 7 grid be tiled using 2 × 1 tiles?
Answer

Yes. It takes 14 tiles.

Number of unit squares = 4 × 7 = 28
28 is even ⇒ 28 ÷ 2 = 14 tiles

Rows = 4 (even) ⇒ each column takes 2 vertical tiles
2 tiles × 7 columns = 14 ✓
Why it happens: only one of the two numbers needs to be even. The 7 columns do not matter, because we tile column by column and each column is 4 squares tall — a whole number of vertical tiles. The odd side simply means there are an odd number of columns to fill, which changes nothing.
Check it yourself: try it the other way, filling rows with horizontal tiles. Each row is 7 squares long — odd — so a row cannot be filled by horizontal tiles alone. Vertical tiles are the ones to use here.
Q3.
What about a 5 × 7 grid?
Answer

No — a 5 × 7 grid can never be tiled with 2 × 1 tiles.

Number of unit squares = 5 × 7 = 35
Each tile covers exactly 2 squares
n tiles cover 2n squares, and 2n is always even

But 35 is odd
⇒ no number of tiles can cover exactly 35 squares
⇒ tiling is impossible
Why it happens: this is a counting argument, not a drawing argument. We do not have to try all the arrangements and fail; we show in one line that every arrangement must fail. Whatever a tile does, it always takes two squares, so the squares covered are always an even number. An odd region is out of reach from the start.
Tip: 17 tiles cover 34 squares and 18 tiles cover 36. There is nothing in between, so 35 can never be hit.
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